The ability of neurons to produce spontaneous spiking depends on several
small depolarizing currents activated at subthreshold voltages, such as the
steady-state persistent sodium current, INaP, and the
hyperpolarization-activated cyclic nucleotide-gated current, Ih. B5
neurons from the buccal ganglion of the pond snail Helisoma trivolvis, grown physically isolated in single cell
culture, fire spontaneous tonic action potentials (APs) [1]. Using whole-cell
recordings in current-clamp and voltage-clamp modes, there is preliminary
evidence that B5 neurons have a TTX-insensitive INaP that is
activated between -60 mV and -40 mV, low- and high voltage-activated Ca2+
currents, Ca2+-dependent K currents mediated via BK and SK channels,
and a strong hyperpolarization-activated cation channel mediating Ih
[1 and unpublished results]. In addition, B5 neurons are capable of generating
Ca2+-dependent evoked APs in the absence of sodium ions [1].

Here we report initial results of modeling experiments, in which we used
spike trains obtained from current clamp recordings as a template for a
computerized modeling approach to characterize the contribution of individual
ion conductances to spontaneous and evoked spike generation in B5 neurons.

For simulations, we used Matlab ODE code following the comprehensive
description of [2]. Our model included the following ionic components: (1)
persistent Na current( INaP); (2) fast sodium current INa(fast);
(3) Delayed rectifying K+ current; (4) N-type Ca2+- current; (5) Small conductance
calcium-activated K current (SK), and (6) hyperpolarization-activated current
(Ih). The channel parameters in the model were hand-tuned to
visually match the experimentally observed recordings of the membrane
potential. We also modeled the influence of APs on the intracellular Ca
concentration using a leaky integrator.

Modeling analysis confirmed the critical role of INaP
in the generation of the spontaneous tonic firing activity. In the absence of INaP in the
model (Ab), there was no spontaneous spiking when compared to the control (Aa),
but APs could still be elicited through simulated current injection. When fast
Na+ channels were removed from the model, B5 neurons continued to
generate spontaneous and evoked spikes (Bb vs. Ba), supporting the notion that
the APs were Ca mediated. Ih is characterized by its distinct
sag-type response to hyperpolarizing current injection (Ca), and this current
is absent when removed from the model (Cb).
While Ih has been found to drive pacemaking activity in some
mammalian neurons, elimination of Ih in B5 neurons did not block,
but merely slowed spontaneous spiking in the model. Rebound spiking, occurring
immediately after being released from a hyperpolarizing current injection is
usually considered to depend on Ih. Rebound spiking in the model
could not be fully explained by Ih, because some rebound spikes were
still present without Ih in the model (Ca vs. Cb). Our model
suggested another explanation for the hyperpolarization-induced increase in
neuronal excitability. Modeling of the intracellular Ca concentration showed a
marked reduction in the intracellular Ca2+ concentration (Db)
induced by the hyperpolarizing current injection (Da). The decrease in
intracellular Ca would be expected to cause the closing of Ca-activated K
channels, resulting in an increase in excitability and causing rebound spiking.
This prediction provides a testable hypothesis for the future electrophysiology
experiments.

The work was supported
by the RAS Presidium Program “Basic Sciences for Medicine” grant to W.D.B.,
and by NSF grant 0843173 to V.R. V.K. and W.D.B. were also partly supported by Federal Target Program “Scientific and scientific-pedagogical personnel of innovative Russia in 2009-2013” (contract no. P812).

Modeled recordings of B5 neurons. A: depolarizing current (1 nA, 1s) was injected in the middle of the trace with INaP (a) and without INaP (b) in the model. B: depolarizing current (1 nA, 1s) was injected in the middle of recording with INa(fast) (a) and without INa(fast) (b) in the model. C: hyperpolarizing current (-.2 nA, 5 s) was injected in the middle of recording with Ih (a) and without Ih (b) in the model. D: (a) - same as C(a), (b) - time course of intracellular [Ca2+] in (a). Note that each AP adds an incremental amount to the overall intracellular [Ca2+]. Record duration in all figures: 12 s. Vertical record span (in mV): A and B: [-80, +80]; C(a): [-60, +60]; C(b): [-80, +60]; D(a): [-60,+60], D(b): Ca2+ concentration in arbitrary units.